Symbol-level network coding for wireless mesh networks
Proceedings of the ACM SIGCOMM 2008 conference on Data communication
Construction of Large Constant Dimension Codes with a Prescribed Minimum Distance
Mathematical Methods in Computer Science
Code construction for multiple sources network coding
Proceedings of the 2009 MobiHoc S3 workshop on MobiHoc S3
Secure Error-Correction Network Coding in a Randomized Setting
ISA '09 Proceedings of the 3rd International Conference and Workshops on Advances in Information Security and Assurance
Secure network coding for wireless mesh networks: Threats, challenges, and directions
Computer Communications
Training overhead for decoding random linear network codes in wireless networks
IEEE Journal on Selected Areas in Communications - Special issue on network coding for wireless communication networks
Bounds on covering codes with the rank metric
IEEE Communications Letters
Error-correcting codes in projective spaces via rank-metric codes and Ferrers diagrams
IEEE Transactions on Information Theory
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Construction and covering properties of constant-dimension codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Decoder error probability of bounded distance decoders for constant-dimension codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Fast encoding and decoding of Gabidulin codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Packing and covering properties of subspace codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Design of efficient robust network codes for multicast connections
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
On noncoherent correction of network errors and erasures with random locations
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Rate regions for coherent and noncoherent multisource network error correction
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
An algebraic watchdog for wireless network coding
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Compressed network coding vectors
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
On the capacity of non-coherent network coding
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Multishot codes for network coding: bounds and a multilevel construction
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
On metrics for error correction in network coding
IEEE Transactions on Information Theory
Convolutional codes for network-error correction
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
Pruning network coding traffic by network coding: a new class of max-flow algorithms
IEEE Transactions on Information Theory
On counteracting byzantine attacks in network coded peer-to-peer networks
IEEE Journal on Selected Areas in Communications
Packing and covering properties of subspace codes for error control in random linear network coding
IEEE Transactions on Information Theory
Diversity-rate trade-off in erasure networks
INFOCOM'10 Proceedings of the 29th conference on Information communications
Constant-rank codes and their connection to constant-dimension codes
IEEE Transactions on Information Theory
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
Robust network coding in the presence of untrusted nodes
IEEE Transactions on Information Theory
Communication over finite-field matrix channels
IEEE Transactions on Information Theory
Recursive code construction for random networks
IEEE Transactions on Information Theory
On (Partial) unit memory codes based on Gabidulin codes
Problems of Information Transmission
Robust network codes for unicast connections: a case study
IEEE/ACM Transactions on Networking (TON)
List decoding subspace codes from insertions and deletions
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Joint network/channel decoding for heterogeneous multi-source/multi-relay cooperative networks
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
An authentication code against pollution attacks in network coding
IEEE/ACM Transactions on Networking (TON)
Automatica (Journal of IFAC)
Revisiting a secret sharing approach to network codes
ProvSec'12 Proceedings of the 6th international conference on Provable Security
Compressed error and erasure correcting codes via rank-metric codes in random network coding
International Journal of Communication Systems
SenseCode: Network coding for reliable sensor networks
ACM Transactions on Sensor Networks (TOSN)
Fast decoding of Gabidulin codes
Designs, Codes and Cryptography
A complete characterization of irreducible cyclic orbit codes and their Plücker embedding
Designs, Codes and Cryptography
Rank subcodes in multicomponent network coding
Problems of Information Transmission
List decoding reed-solomon, algebraic-geometric, and gabidulin subcodes up to the singleton bound
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
New construction of error-tolerant pooling designs
Information Theory, Combinatorics, and Search Theory
Asymptotic behaviour of codes in rank metric over finite fields
Designs, Codes and Cryptography
Hi-index | 755.32 |
The problem of error-control in random linear network coding is considered. A ldquononcoherentrdquo or ldquochannel obliviousrdquo model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer characteristic. Motivated by the property that linear network coding is vector-space preserving, information transmission is modeled as the injection into the network of a basis for a vector space V and the collection by the receiver of a basis for a vector space U. A metric on the projective geometry associated with the packet space is introduced, and it is shown that a minimum-distance decoder for this metric achieves correct decoding if the dimension of the space V capU is sufficiently large. If the dimension of each codeword is restricted to a fixed integer, the code forms a subset of a finite-field Grassmannian, or, equivalently, a subset of the vertices of the corresponding Grassmann graph. Sphere-packing and sphere-covering bounds as well as a generalization of the singleton bound are provided for such codes. Finally, a Reed-Solomon-like code construction, related to Gabidulin's construction of maximum rank-distance codes, is described and a Sudan-style ldquolist-1rdquo minimum-distance decoding algorithm is provided.